For every simulated atmospheric profile and on-sky telemetry we find that both predictors provide an improvement over a classic integrator. PFC provides a consistent improvement of 2-3 over the integrator, while EOF shows more variety. EOF succeeds more notably in picking out one extremely fast wind layer (the single-layer 14 m/s atmosphere), but requires a longer training set (90000 frames of data) to find and remove the 7 m/s wind layer. In contrast, PFC performs consistently with only 10000 frames of training data. Both methods of predictive control also out-perform the integrator in the on-sky telemetry example, which is consistent with the results of Jensen-Clem (2019)[1]}. For the on-sky telemetry, we find that PFC shows a greater improvement than EOF, in contrast with its performance over the simulated atmospheres. This may be indicative of the way a Kalman filter handles Gaussian noise (a Kalman filter carries the variance of a distribution in its covariance matrix through each iteration[2]}), as opposed to the treatment of EOF as a purely linear filter. While EOF shows greater performance consistently over atmospheric simulation (which includes no measurement noise), the comparative performance over telemetry may better forecast lab and on-sky performance of the two predictors. However, between the two methods, EOF is less complex to implement, as evinced by the length of Appendix .
